Related papers: Cosh gradient systems and tilting
Multiple studies of neural avalanches across different data modalities led to the prominent hypothesis that the brain operates near a critical point. The observed exponents often indicate the mean-field directed-percolation universality…
We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is…
The theory of slow-fast gradient systems leads in a natural way to non-equilibrium steady states, because on the slow time scale the fast subsystem stays in steady states that are controlled by the interaction with the slow system. Using…
We study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap. We consider a scaling in which the number of particles tends to infinity while the volume fraction of the rods…
Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions $\mathscr L$ that induce a flow, given by $\mathscr L(\rho_t,\dot\rho_t)=0$. We derive necessary and…
Living cells use phase separation and concentration gradients to organize chemical compartments in space. Here, we present a theoretical study of droplet dynamics in gradient systems. We derive the corresponding growth law of droplets and…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…
We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the…
A fully quantum mechanical description of the precessional damping of Pt/Co bilayer is presented in the framework of the Keldysh Green function approach using {\it ab initio} electronic structure calculations. In contrast to previous…
Driven-dissipative many-body systems are difficult to analyze analytically due to their non-equilibrium dynamics, dissipation and many-body interactions. In this paper, we consider a driven-dissipative infinite-range Ising model with local…
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a notion of evolutionary Gamma-convergence that relates the…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
A foundational question in relativistic fluid mechanics concerns the properties of the hydrodynamic gradient expansion at large orders. We establish the precise conditions under which this gradient expansion diverges for a broad class of…
The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other.…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We study the quantum dynamics of a number of model systems as their coupling constants are changed rapidly across a quantum critical point. The primary motivation is provided by the recent experiments of Greiner et al. (Nature 415, 39…
Dynamics of a dissipative two-level system is studied using quantum relaxation theory. This calculation for the first time goes beyond the commonly used dilute bounce gas approximation (DBGA), even for strong damping. The new results…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…